RE: Determinism, Free Will and Paradox
January 20, 2015 at 11:46 am
(This post was last modified: January 20, 2015 at 11:53 am by Alex K.)
(January 20, 2015 at 11:38 am)bennyboy Wrote:(January 20, 2015 at 10:50 am)Alex K Wrote: Again, as I said above, the geometry of special relativity has a defined causal structure even if there is no absolute standard of time scale, and I think this collapse to a singularity is merely an artifact of choosing a mathematically divergent coordinate systemDivergence is beyond my level of understanding in math. Can you explain it in principle?
en.wikipedia.org/wiki/Spacetime
It's nothing complicated. Imagine you define your own measurement system for lengths, and call it a bennymeter. You introduce a parameter x and you define a bennymeter to have x meters. You can now ask what is the height of the Eiffel tower, and if you take x = 1, the answer will be roughly 300 bennymeters. If you choose x=1/2 it will be 600 bennymeters. If you take x=0 it will be infinity bennymeters, or, more precisely, as you approach x->0, your measurement will give you arbitrarily large numbers of bennymeters as the height of the eiffel tower, or as the height of anything for that matter. In the limit x->0 your measurement is divergent. That means x=0 is a pathological coordinate choice.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
